An Algorithm for Constructing Gröbner and Free Schreier Bases in Free Group Algebras
✍ Scribed by Amnon Rosenmann
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 915 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
✦ Synopsis
We present an algorithm for computing Gröbper and free canonical Schreier bestes for finitely generated ono-sided ideals in free group algebras. That is, given a zet of (n) elements of a free group algebra, we construct a canonical Schrejer basie of free generators as well an a Gröbnar basis for the right ideal generated by the original ett. In contrast to Buchberger's algorithm in polynomial rings, at any stage the eurrent nuraber of polynomiale does not exceed (2 n) and their maximal degree ia bounded by (d+1), where (d) is the maximal degree of the original polynomiale.
A corollary is that the generalised memberxhip problem for free group algebras is solvsble.
As a apecial case we obtain an algarithm wimilar to the Nieleen.Hall algorithm for constructing free baces for tubgroups of free groups.
A generalisation of the notion of a Gröbner bacia is given by the defaition of algebras eakiafying constructive diviwion algorithms.